33 - Diagonalization
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Practice Questions
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What is the condition for a matrix to be diagonalizable?
💡 Hint: Consider the relationship between eigenvalues and the independence of eigenvectors.
Define eigenvalue in your own words.
💡 Hint: Think about what happens to vectors when transformed by matrices.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does it mean for a matrix to be diagonalizable?
💡 Hint: Think of the properties of the eigenvectors.
True or False: All matrices with repeated eigenvalues are non-diagonalizable.
💡 Hint: Consider examples of matrices with distinct eigenvalues.
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Challenge Problems
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Given the matrix A = [2 3; 2 4], demonstrate if A is diagonalizable and find its eigenvalues and eigenvectors.
💡 Hint: Focus on the linearly independent nature of the eigenvectors.
Prove the Jordan form is useful for non-diagonalizable matrices by providing an example and explaining the process.
💡 Hint: Think about the roles of blocks in Jordan form.
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